Estimation effects on powers of two simple test statistics in identifying an outlier in linear models

Abstract

In this paper, we consider two well known, namely the maximum studentized residual (MSR) and maximum normed residual (MNR), test statistics for the detection of a single outlier in linear models. The regression and variance parameters involved in the test statistics are estimated by the traditional least square method (LSM) as well as by two different robust methods (RMs). It is shown through a simulation study that even though RM when compared with LSM produces better estimates for the parameters of the model in the presence of an outlier, the robust estimates-based MSR and MNR tests are however found to be equally or less powerful than the LS estimates-based MSR and MNR tests. This suggests that one should use the LS estimates-based test for the detection of an outlier. Next, if the LS estimates-based test confirms the presence of an outlier, one should however estimate the parameters by using RM.

Keywords:

• Design matrix
• Location of outlier
• Least square and robust estimates
• p-value
• Pseudo-F statistics
• Size and power of the test
• Variance-inflated outlier

Acknowledgements

This research was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada. The authors would like to thank the referee for his valuable comments on an earlier version.